List questions from alternative-proof

Published on 30 Dec 2017 - 17:55

57

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Question regarding bijection such that $f(x) \neq x$

Published on 01 Jan 2018 - 12:43

69

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Proof with Baire category theorem that the set $(0,1)$

Published on 02 Jan 2018 - 10:41

344

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Finite ring with unity has $ab=1_R\implies ba=1_R$ for $a,b\in R$

Published on 12 Apr 2026 - 19:03

4.2k

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Layman's proof that the area of a circle of radius $r$ equals $\pi r^2$.

Published on 05 Jan 2018 - 17:08

180

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Prove that $\sum^m_{k=0}\binom{m}{k}(-1)^k(\frac{1}{n+k+1}) = \frac{m!n!}{(m+n+1)!}$

Published on 07 Jan 2018 - 19:58

68

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Show that $f(x,y) = (x^2y-\frac13y^3, \frac13x^3-xy^2)$ is totally differentiable and calculate its derivative.

Published on 08 Jan 2018 - 13:22

1.1k

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A Ramanujan sum involving $\sinh$

Published on 09 Apr 2026 - 13:34

580

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An interesting identity involving Jacobi $\theta_4$ and $\zeta(2)$

Published on 26 Mar 2026 - 12:37

3.4k

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Proofs that every natural number is a sum of four squares.

Published on 13 Apr 2026 - 0:27

12.5k

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The Hexagonal Property of Pascal's Triangle

Published on 29 Mar 2026 - 19:09

16.3k

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Help understand the proof of infinitely many primes of the form $4n+3$

Published on 10 Feb 2011 - 7:59

284

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Regarding a proof involving geometric series

Published on 11 Apr 2026 - 14:40

465

Views

Tropical Lifting Lemma (Puiseux Series)

Published on 07 Apr 2011 - 13:39

6.6k

Views

$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?

Published on 08 Apr 2026 - 23:07

List Question

Question regarding bijection and inverses

Question regarding bijection such that $f(x) \neq x$

Proof with Baire category theorem that the set $(0,1)$

Finite ring with unity has $ab=1_R\implies ba=1_R$ for $a,b\in R$

Layman's proof that the area of a circle of radius $r$ equals $\pi r^2$.

Prove that $\sum^m_{k=0}\binom{m}{k}(-1)^k(\frac{1}{n+k+1}) = \frac{m!n!}{(m+n+1)!}$

Show that $f(x,y) = (x^2y-\frac13y^3, \frac13x^3-xy^2)$ is totally differentiable and calculate its derivative.

A Ramanujan sum involving $\sinh$

An interesting identity involving Jacobi $\theta_4$ and $\zeta(2)$

Proofs that every natural number is a sum of four squares.

The Hexagonal Property of Pascal's Triangle

Help understand the proof of infinitely many primes of the form $4n+3$

Regarding a proof involving geometric series

Tropical Lifting Lemma (Puiseux Series)

$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?

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